Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 30000)	Who ?	When ?
8001	(29*10^57967+673)/9	57968	Robert Price	10/2017
8002	(3^121492-5)/4	57966	Lelio R Paula	03/2012
8003	2^192549+35	57964	Lelio R Paula	04/2011
8004	28799!2+2	57962	Robert Price	10/2012
8005	(7*2^192534-1)/1347	57957	Lelio R Paula	01/2014
8006	7001^15069-100	57943	Enzo Doria	07/2012
8007	L(277273)/11090921	57940	Donovan Johnson	11/2005
8008	(2^192469-1017)/35	57938	Lelio R Paula	02/2012
8009	2^192457-1155*192457	57936	Henri Lifchitz	02/2005
8010	2^192443+1385	57932	Lelio R Paula	05/2011
8011	132^27317-131	57928	Norbert Schneider	03/2015
8012	41522!3-59049	57912	Robert Price	12/2015
8013	(3*2^192380-1)/169	57911	Lelio R Paula	01/2014
8014	2^192339-2515	57900	Yves Minet	07/2014
8015	2^192303+7695	57889	Lelio R Paula	10/2012
8016	2^192273-5955	57880	Lelio R Paula	05/2011
8017	2^192257+16095	57876	Lelio R Paula	05/2011
8018	109^28401-2	57865	Lelio R Paula	10/2017
8019	2^192218-111861	57864	Enzo Doria	05/2014
8020	2^192214-3941	57863	Yves Minet	04/2017
8021	(2^192212+3)/259	57860	Lelio R Paula	02/2012
8022	(3^121270+8)/155939753	57853	Lelio R Paula	03/2012
8023	80^30393-79	57841	Norbert Schneider	03/2015
8024	20^44455-3123	57838	Enzo Doria	03/2013
8025	2^192122-195	57835	Lelio R Paula	04/2011
8026	(29*10^57834+91)/3	57835	Robert Price	03/2016
8027	8*6^74306+5	57823	Lelio R Paula	09/2014
8028	(39^36341-1)/38	57820	Robert Price	04/2012
8029	2^192037-111805	57809	Enzo Doria	05/2014
8030	2^192023-192023^2	57805	Henri Lifchitz	05/2005
8031	21^43717+2	57804	Ray Chandler	08/2011
8032	8*5^82687+7	57797	Lelio R Paula	09/2014
8033	5^82680-24	57791	Lelio R Paula	10/2012
8034	(2^191915+47)/95	57771	Lelio R Paula	02/2012
8035	(74*10^57763+133)/9	57764	Robert Price	10/2017
8036	6^74227-95	57760	Lelio R Paula	10/2012
8037	2^191861+29835	57756	Lelio R Paula	10/2012
8039	1908^17605+17605^1908	57755	Serge Batalov	05/2014
8038	5*10^57754+59	57755	Robert Price	09/2016
8040	(5*2^191821-1)/8924067	57738	Lelio R Paula	01/2014
8041	38^63917+5^63917-34^63917+3*2^63917	57724	Mike Oakes	11/2010
8042	41399!3-6561	57723	Robert Price	11/2015
8043	2^191745+17	57721	Lelio R Paula	04/2011
8044	2^191730-761	57717	Yves Minet	01/2012
8045	(2^191733-3)/2251	57715	Lelio R Paula	02/2012
8046	2^191698-111	57707	Lelio R Paula	04/2011
8047	(13*10^57691+23)/9	57692	Robert Price	02/2015
8048	20^44340-5423	57688	Enzo Doria	03/2013
8049	(27*2^191629+1)/125	57686	Lelio R Paula	07/2012
8050	410^57684+37^57684	57685	Mike Oakes	11/2010
8051	2*3^120898+5	57684	Lelio R Paula	04/2014
8052	(6883*2^191610-1)/7347	57681	Lelio R Paula	04/2015
8053	6^74117-49	57675	Lelio R Paula	10/2012
8054	2^191586-113201	57674	Enzo Doria	07/2014
8055	2^191580+193	57672	Lelio R Paula	04/2011
8056	(103*29^39433+10401)/4	57669	Curtis Bright	05/2015
8057	2^191560+255255	57666	Lelio R Paula	05/2011
8058	2^191515-85	57652	Lelio R Paula	04/2011
8059	2^191502-1127	57648	Yves Minet	05/2013
8060	2*5^82473-3^82473	57647	Mike Oakes	08/2010
8061	(13*10^57634-61)/3	57635	Robert Price	08/2017
8062	2^191430+103	57627	Lelio R Paula	04/2011
8063	3*2^191408+5	57621	Lelio R Paula	03/2014
8064	2^191382-1858931	57612	Enzo Doria	04/2016
8065	6*7^68163+5	57606	Lelio R Paula	09/2014
8066	91^29403-2	57602	Lelio R Paula	08/2013
8067	11^55308-7950	57598	Enzo Doria	02/2013
8068	2^191329+65	57596	Lelio R Paula	04/2011
8069	11^55302-240	57592	Enzo Doria	07/2012
8070	2^191299-1031467	57587	Paul Bourdelais	11/2012
8071	2^191295-111991	57586	Enzo Doria	05/2014
8072	2^191279-1297	57581	Yves Minet	08/2012
8073	3*6^73961+5	57554	Lelio R Paula	09/2014
8074	(3^120623+5)/52144	57548	Lelio R Paula	04/2012
8075	(17*10^57543-29)/3	57544	Robert Price	09/2017
8076	42^35445-41	57537	Norbert Schneider	06/2014
8077	(71^31079-1)/70	57534	Paul Bourdelais	08/2017
8078	2^191069-723403	57518	Paul Bourdelais	11/2012
8079	4*10^57506-3	57507	Serge Batalov	11/2010
8080	10^57501+67359	57502	Patrick De Geest	06/2016
8081	10^57501-1000000001	57501	Robert Price	05/2016
8082	10^57501-249861	57501	Patrick De Geest	06/2016
8083	(9^60251+4^60251)/13	57493	Robert Price	02/2013
8084	20^44184-6003	57485	Enzo Doria	03/2013
8085	2^190948+12705	57482	Lelio R Paula	10/2012
8086	2^190945+29	57481	Henri Lifchitz	06/2005
8087	2^190922-401	57474	Yves Minet	01/2012
8088	15^48860+46	57464	Lelio R Paula	02/2013
8089	3^120434+20	57462	Lelio R Paula	10/2012
8090	7^67964-38	57437	Lelio R Paula	10/2012
8091	2^190799-113065	57437	Enzo Doria	07/2014
8092	9*5^82159+2	57428	Lelio R Paula	09/2014
8093	(F(22898)^13-F(22897)^13)/F(22896)	57422	Wayne Halsdorf	03/2012
8095	lucasU(432,25,21787)-5*lucasU(432,25,21786)	57416	Mike Oakes	05/2009
8094	(103*10^57414-1)/3	57416	Serge Batalov	12/2014
8096	(1654*30^38869-1)/29	57416	Karsten Bonath	05/2017
8097	2*10^57410+9^57410	57411	Mike Oakes	04/2011
8098	2^190704-1595	57408	Lelio R Paula	05/2011
8099	11^55121-1740	57403	Enzo Doria	11/2012
8100	2^190644-185	57390	Lelio R Paula	04/2011
8101	41182!3-3^41182	57389	Robert Price	08/2015
8102	2^190629-112255	57386	Enzo Doria	06/2014
8103	(2*10^57384-71)/3	57384	Robert Price	01/2017
8105	2*6^73735+5^73735	57378	Mike Oakes	11/2009
8104	2^190605+59	57378	Lelio R Paula	04/2011
8106	6^73727-7	57371	Lelio R Paula	10/2012
8107	2^190561-112225	57365	Enzo Doria	06/2014
8108	10^57358+170899	57359	Patrick De Geest	06/2016
8109	10^57358-8001	57358	Robert Price	03/2016
8110	18^45687-11	57350	Lelio R Paula	02/2013
8111	11^55069-210	57349	Enzo Doria	07/2012
8112	11^55068-12	57348	Lelio R Paula	02/2013
8113	19^44839+54	57339	Lelio R Paula	02/2013
8115	(7*2^190468-1)/8511	57334	Lelio R Paula	01/2014
8114	(23*10^57333-59)/9	57334	Robert Price	03/2017
8116	2^190455-1155*190455	57333	Henri Lifchitz	02/2005
8117	65^31620+28	57325	Lelio R Paula	01/2016
8118	2^190403+16095	57318	Lelio R Paula	05/2011
8119	(19*10^57316+119)/3	57317	Robert Price	02/2017
8120	(21*2^190393+1)/211	57314	Lelio R Paula	07/2012
8121	2^190392-112025	57314	Enzo Doria	05/2014
8122	(24737*2^190234+1)/9	57270	Lelio R Paula	05/2014
8123	(7*2^190230+1)/23	57265	Lelio R Paula	07/2012
8124	(10223*2^190197+1)/3211	57256	Lelio R Paula	05/2014
8125	18^45590-97	57228	Lelio R Paula	02/2013
8126	(3*2^190105-1)/19205	57224	Lelio R Paula	01/2014
8127	(16*10^57219-31)/3	57220	Robert Price	03/2016
8128	(2^190074+47)/51	57217	Lelio R Paula	02/2012
8129	3^119894-140	57204	Lelio R Paula	10/2012
8131	(37^36473-1)/36	57196	Robert Price	03/2012
8130	2^190000-2163	57196	Yves Minet	08/2013
8132	2^189987-2798107	57192	Enzo Doria	04/2016
8133	2^189935-112117	57177	Enzo Doria	05/2014
8134	2^189909-112231	57169	Enzo Doria	06/2014
8135	132049#+149053	57161	Makoto Morimoto	12/2015
8136	41032!3-27	57158	Robert Price	09/2014
8137	19^44694+22	57153	Lelio R Paula	02/2013
8138	12^52956-17	57150	Lelio R Paula	02/2013
8139	2^189823-967	57143	Yves Minet	01/2012
8140	(25*10^57138-61)/9	57139	Robert Price	02/2015
8141	5^81743-4^(81743+1)	57136	Robert Price	04/2016
8142	7^67593-54	57123	Lelio R Paula	10/2012
8143	7*3^119712+2	57118	Lelio R Paula	03/2014
8144	5^81700+16	57106	Lelio R Paula	10/2012
8145	2^189700+76561	57106	Enzo Doria	05/2016
8146	2^189671+131	57097	Lelio R Paula	04/2011
8147	4*6^73374+5	57097	Lelio R Paula	09/2014
8148	(67607*2^189651+1)/43727	57091	Lelio R Paula	05/2014
8149	(29*2^189619-1)/393	57080	Lelio R Paula	01/2014
8150	3^119587+80	57058	Lelio R Paula	10/2012
8151	2^189502-113453	57046	Enzo Doria	07/2014
8152	2^189455+153	57032	Lelio R Paula	04/2011
8153	24^41317-41317^24	57027	Norbert Schneider	07/2016
8154	2^189414-17	57020	Lelio R Paula	03/2011
8155	24^41311+23	57018	Norbert Schneider	12/2013
8156	(4*10^56989-31)/9	56989	Erik Branger	05/2011
8157	11^54712-1620	56977	Enzo Doria	11/2012
8158	2^189237-112231	56967	Enzo Doria	06/2014
8159	17^46285-48	56952	Lelio R Paula	02/2013
8160	2^189188+75241	56952	Enzo Doria	04/2016
8161	2^189181+94395	56950	Henri Lifchitz	01/2005
8162	7001^14808-108	56940	Enzo Doria	07/2012
8163	2^189147-112639	56939	Enzo Doria	06/2014
8164	2^189110-3	56928	M. Frind & P. Underwood	11/2002
8165	2^189069+12909	56916	Lelio R Paula	04/2011
8166	(13*10^56909+191)/3	56910	Robert Price	08/2017
8167	(35*10^56898-17)/9	56899	Serge Batalov	02/2009
8168	2^189011-5955	56898	Lelio R Paula	04/2011
8169	6^73119-5	56898	Lelio R Paula	10/2012
8170	13^51076-90	56896	Lelio R Paula	02/2013
8171	2^188997+56897	56894	Yves Minet	02/2010
8172	5^81388-13766	56888	Enzo Doria	02/2013
8173	20^43713-6403	56872	Enzo Doria	03/2013
8174	(71*10^56858-287)/9	56859	Robert Price	05/2017
8175	2^188857-254233	56852	Gary Barnes	09/2009
8177	15^48338-88	56850	Lelio R Paula	02/2013
8176	10^56849+136437	56850	Patrick De Geest	07/2017
8178	10^56849-701	56849	Robert Price	06/2017
8179	(2^188788+78557)/3	56831	Lelio R Paula	05/2012
8180	2^188771+16095	56826	Lelio R Paula	04/2011
8181	7*2^188742-9	56818	Lelio R Paula	03/2014
8182	12^52646-65	56815	Lelio R Paula	02/2013
8183	5003^15358-158	56813	Enzo Doria	07/2012
8184	2^188713+577294575	56809	Lelio R Paula	03/2013
8185	2^188693-112099	56803	Enzo Doria	05/2014
8186	(7^67211+4^67211)/11	56799	Robert Price	10/2012
8187	2^188678-94395	56798	Lelio R Paula	09/2011
8188	20^43651-8503	56792	Enzo Doria	03/2013
8189	2^188657-2371	56792	Yves Minet	10/2013
8190	(14^49549+5^49549)/19	56789	Robert Price	05/2013
8191	(45^34351-1)/44	56788	Robert Price	05/2014
8192	7*10^56785-23	56786	Robert Price	04/2016
8193	(10^56781-31)/3	56781	Serge Batalov	12/2014
8194	7*10^56779+3	56780	Erik Branger	11/2009
8195	10^56765+259179	56766	Patrick De Geest	09/2013
8196	10^56765-249497	56765	Patrick De Geest	09/2013
8197	t(188706)	56764	Robert Price	04/2015
8198	2^188551-904327	56760	Paul Bourdelais	11/2012
8199	(64*10^56756+17)/9	56757	Robert Price	09/2015
8200	131101#+146291	56757	Makoto Morimoto	02/2016
8201	2^188539-112519	56756	Enzo Doria	06/2014
8202	6^72927+101	56749	Lelio R Paula	10/2012
8203	20^43617-1603	56748	Enzo Doria	03/2013
8204	(3^118892-8)/91358929	56718	Lelio R Paula	03/2012
8205	(509203*2^188338-1)/3	56701	Lelio R Paula	03/2015
8206	20^43567-5623	56682	Enzo Doria	03/2013
8207	2^188234-113183	56665	Enzo Doria	07/2014
8208	(7*2^188215-1)/1497315125	56651	Lelio R Paula	01/2014
8209	(1017*2^188171-1)/35	56647	Lelio R Paula	03/2015
8210	(34*10^56647-7)/9/37/263	56644	Makoto Morimoto	04/2016
8211	(2^188176-1017)/453814543	56638	Lelio R Paula	02/2012
8212	33*10^56634+7	56636	Robert Price	07/2016
8214	(F(31)^9241-F(30)^9241)/F(29)	56634	Wayne Halsdorf	08/2010
8213	14^49413+33	56634	Lelio R Paula	02/2013
8215	3^118680+110	56625	Lelio R Paula	10/2012
8216	(13*10^56624+161)/3	56625	Robert Price	04/2017
8217	(3^118676-2)/7516653263	56613	Lelio R Paula	03/2012
8218	(13*2^188062+1)/17	56613	Lelio R Paula	07/2012
8219	2^188056-1313	56611	Yves Minet	08/2012
8220	20^43510-5583	56608	Enzo Doria	03/2013
8221	2^188032+12285	56604	Lelio R Paula	03/2011
8222	(265*10^56588+17)/3	56590	Robert Price	05/2016
8223	2^187959+5775	56582	Lelio R Paula	03/2011
8224	(5*2^187959+1)/53	56581	Lelio R Paula	07/2012
8225	(11*2^187889-1)/351	56559	Lelio R Paula	01/2014
8226	(100049^11311+1)/100050	56553	Faysal YAtim	09/2007
8227	(19*10^56544-1)/9	56545	Serge Batalov	03/2009
8228	20^43447-8923	56526	Enzo Doria	03/2013
8229	2^187743-112177	56517	Enzo Doria	06/2014
8230	(F(5879)^47-F(5878)^47)/F(5877)	56502	Wayne Halsdorf	08/2010
8231	5^80831-22	56499	Lelio R Paula	10/2012
8232	5^80828-13166	56497	Enzo Doria	02/2013
8233	7*2^187590-5	56472	Lelio R Paula	03/2014
8234	2^187555+75473	56460	Enzo Doria	04/2016
8235	2^187541-283	56456	Yves Minet	01/2012
8236	(55*10^56453-1)/9	56454	Serge Batalov	03/2009
8237	2^187506-1451	56445	Yves Minet	08/2012
8238	189^24794-2	56443	Lelio R Paula	10/2017
8239	6^72522+143	56434	Lelio R Paula	10/2012
8240	(15185*2^187452-1)/949	56430	Lelio R Paula	03/2015
8241	2^187390+79	56411	Lelio R Paula	03/2011
8242	2^187386+12909	56409	Lelio R Paula	03/2011
8243	2^187382+613	56408	Jason Earls	04/2008
8244	(34*10^56392-7)/9/37/883/23887	56384	Makoto Morimoto	04/2016
8245	20^43337-9	56383	Lelio R Paula	02/2013
8246	(F(1008)^269-F(1007)^269)/F(1006)	56364	Wayne Halsdorf	08/2010
8247	2^187230+427	56362	Henri Lifchitz	01/2005
8248	11^54121-9480	56362	Enzo Doria	02/2013
8249	(21*2^187202-1)/43	56354	Lelio R Paula	01/2014
8250	2^187173-91	56345	Lelio R Paula	03/2011

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PRP Records

Probable Primes Top 10000

(183432 PRPs in the top)